As is known in the art, variable gain amplifiers are used in a wide range of applications. One such application is in transducer array systems, such as, for example, ultrasound imaging, sonar, and radar. With such systems, pulses of wave energy are transmitted and are returned as echo signals to a receiver. More particularly, the electrical signals produced in response to reception of the echo signals are converted into electrical signals and are then fed to amplifiers for post-processing signal conditioning. As is known in the art, such amplifiers may include a time gain control wherein the gains of the amplifiers are adjusted as a function of the time after transmission of the echo pulse; i.e., the amplifiers have gain variations as a function of time, i.e., time gain control.
In many applications it is required that the gain of the amplifiers be adjusted as an exponential (i.e., as a linear natural logarithmic) function of time. For example, in some ultrasound applications, it is highly desirable to control the gain in a variable gain amplifier (VGA) which grows exponentially with the control signal; i.e. 50 dB of gain change for every 1 volt change in the control signal. This allows the control signal to exist in a reasonable range of signals for a very wide range in gain change (>40 dB or factor greater than 100). Active or passive signal interpolative methods have been used in the past with gain controllers. Control is achieved by manipulating the level of interpolation. For example, a programmable resistor divider can be used to attenuate the signal depending upon the selected resistors. The resistor divider would be programmed by switches controlled by some register. Thus using interpolation has the advantage of being very flexible in terms of the gain curve. The points along the gain curve can be manipulated by simply adjusting the register setting.
Another common method of gain control is to generate the control signal using a simple bipolar junction transistor (BJT) which has an inherent exponential response. This is convenient because it intrinsically creates a dB/V curve. FIG. 1 shows a circuit which illustrates this type of controller. The controller is basically Q0. The current I1 is given by Q0 which is equal to
            I      ⁢                          ⁢      1        =                  Is        0            ⁢              ⅇ                              (                          Vcc              -              Vtgc                        )                    Vt                      ,where: Iso is the saturation current; Vcc is the collector voltage, and Vt is equal to kT/q, where k is Boltzmann's constant, q is the charge on the electron and T is absolute temperature in degrees Kelvin (VT evaluates to approximately 26 mV at 300° K.).
The gain of the circuit shown in FIG. 1 is given by
            Vout      /      Iin        =                  (                  1          -                                                    Is                0                            It                        ⁢                          ⅇ                                                Vcc                  -                  Vtgc                                Vt                                                    )            ⁢      Rfb      ⁢                          ⁢      1        ,where Vtgc is the voltage at the base electrode of Q0, i.e., Vbe. This can therefore be approximated as an exponential gain controller.
The interpolative method mentioned above, requires a trade off of range for complexity and size. As the desired controller dynamic range increases, the more programmable switches and interpolative stages are required. This can become costly for large dynamic ranges and where the array of tranducers requires dense amplification channel designs.
While the BJT type of controller of FIG. 1 can handle large ranges, it does not have an ideal exponential curve thus some kind of compensation may be required to handle the portion of the curve which is not exponential. This is due to the constant 1 in the equation
      (          1      -                                    Is            0                    It                ⁢                  ⅇ                                    Vcc              -              Vtgc                        Vt                                )    .The BJT type controller, while compact and cost effective, has temperature effects as well and may not provide the required ideal exponential gain relationship.